Решение
1. Область определения
y = 2cos(x-п/3)
D(y) = R
2. Область значения
- 1 ≤ 2cos(x-п/3) ≤ 1
- 1/2 ≤ cos(x-п/3) ≤ 1/2
1) cos(x-п/3) ≥ - 1/2
- arccos(-1/2) + 2πk ≤ x - п/3 ≤ arccos(-1/2) + 2πk, k ∈ Z
- 2π/3 + 2πk ≤ x - п/3 ≤ 2π/3 + 2πk, k ∈ Z
- 2π/3 + π/3 + 2πk ≤ x ≤ 2π/3 + π/3 + 2πk, k ∈ Z
- π/3 + 2πk ≤ x ≤ π + 2πk, k ∈ Z
2) cos(x-п/3) ≤ - 1/2
arccos(-1/2) + 2πk ≤ x - п/3 ≤ 2π - arccos(-1/2) + 2πk, k ∈ Z
2π/3 + 2πk ≤ x - п/3 ≤ 2π - 2π/3 + 2πk, k ∈ Z
2π/3 + 2πk ≤ x - п/3 ≤ 4π/3 + 2πk, k ∈ Z
2π/3 + π/3 + 2πk ≤ x ≤ 4π/3 + π/3 + 2πk, k ∈ Z
π + 2πk ≤ x ≤ 5π/3 + 2πk, k ∈ Z